Week 8, Day 3 Use equivalent fractions to find percentages. · ã Hamilton Trust Explore more Hamilton Trust Learning Materials at Week 8, Day 3 Use equivalent fractions to find percentages

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Week 8, Day 3 Use equivalent fractions to find percentages.

Each day covers one maths topic. It should take you about 1 hour or just a little more. 1. If possible, watch the PowerPoint presentation with a

teacher or another grown-up.

OR start by carefully reading through the Learning Reminders.

2. Tackle the questions on the Practice Sheet. There might be a choice of either Mild (easier) or Hot (harder)! Check the answers.

3. Finding it tricky? That’s OK… have a go with a grown-up at A Bit Stuck?

4. Think you’ve cracked it? Whizzed through the Practice Sheets?

Have a go at the Investigation…

5. Have I mastered the topic? A few questions to Check

your understanding. Fold the page to hide the answers!


Learning Reminders


Learning Reminders


Learning Reminders

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© Hamilton Trust

Practice Sheet MildComparing percentages

The following new woodlands have been planted:

Burley Common100 trees50% oak, 20% ash, 15% beech, 15% willow

Merttens Meadow300 trees20% oak, 20% hazel, 40% willow, 20% beech

Chidgey Common200 trees40% oak, 30% beech, 10% ash, 20% sweet chestnut

Holes Hollow200 trees25% oak, 10% hazel, 20% willow, 15% beech, 30% ash

Calculate how many trees of each type there are in each of the four woodlands.

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© Hamilton Trust

Practice Sheet HotComparing percentages

The following new woodlands have been planted:

Burley Common100 trees50% oak, 20% ash, 15% beech, 15% willow

Merttens Meadow150 trees20% oak, 20% hazel, 40% willow, 20% beech

Chidgey Common200 trees40% oak, 30% beech, 10% ash, 20% sweet chestnut

Holes Hollow120 trees25% oak, 10% hazel, 15% willow, 30% beech, 20% ash

Calculate how many trees of each type there are in each of the four woodlands.

Challenge

In Weston Wood, there are 280 trees, as follows:14 holly126 lime84 beech56 silver birch.What percentages do these numbers represent?



Practice Sheets Answers

Comparing percentages (mild)

Burley Common has:50 oak, 20 ash, 15 beech and 15 willow.

Merttens Meadow has:60 oak, 60 hazel, 120 willow and 60 beech.

Chidgey Common has:80 oak, 60 beech, 20 ash and 40 sweet chestnut.

Holes Hollow has:50 oak, 20 hazel, 40 willow, 30 beech and 60 ash.

© Hamilton Trust

Comparing percentages (hot)

Burley Common has:50 oak, 20 ash, 15 beech and 15 willow. Merttens Meadow has:30 oak, 30 hazel, 60 willow and 30 beech. Chidgey Common has:80 oak, 60 beech, 20 ash and 40 sweet chestnut. Holes Hollow has:30 oak, 12 hazel, 18 willow, 36 beech and 24 ash.

Challenge

14 holly = 5%126 lime = 45%84 beech = 30%56 silver birch = 20%



© Hamilton Trust

A Bit Stuck?Linking fractions and division

40 ÷ 5 = 1/5 of 40 is

4/5 of 40 is

1/10 of 40 is

7/10 of 40 is

40 ÷ 10 =

40 ÷ 8 =

, so

, so

, so

3/10 of 40 is

1/8 of 40 is

5/8 of 40 is

8/8 of 40 is



Linking fractions and division

40 ÷ 5 = 8, so 1/5 of 40 is 8 4/5 of 40 is 3240 ÷ 10 = 4, so 1/10 of 40 is 4 7/10 of 40 is 28 3/10 of 40 is 1240 ÷ 8 = 5, so 1/8 of 40 is 5 5/8 of 40 is 25 8/8 of 40 is 40

A Bit Stuck? Answers

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InvestigationPercentage puzzles

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%+ ? = x cm³ ½ ÷ £ ⅓ > m² + % < ⅚ – cm ? × ÷< ⅓

+ ? = x cm³ ½ ÷ £ ⅓ > m² + % < ⅚ – cm ? × ÷< ⅓

© Hamilton Trust

Challenge

A shopkeeper has some coats he wants to sell. He can give each coat a price anywhere between £30 and £100 but he must make sure he sells each coat for at least £40. If he wants it to look good, what is the best way of advertising a percentage reduction?

1. Find 10% of £40.Find 40% of £10.Compare these amounts.

2. Find 20% of £60.Find 60% of £20.Compare these amounts.

3. Find 15% of £50.Find 50% of £15.

Discuss what you have noticed. Can you explain this?

Find the matching question for each of these:

25% of £40 30% of £90 5% of £50? % of £? ? % of £? ? % of £?

cm³




Check your understanding Questions

Is 10% larger or smaller than 1/5? Explain your answer with a picture or calculation.

Write the missing percentage in each of the bar models:

Now write the numbers of children in each category.

Write 10% of each price, then calculate 40% of each price.

60 children

Walk 20%

Cycle 50% Drive ?

24 children Crisps 75%

Fruit ?

£3.40 £12.00 £9.90 £5.10


Check your understanding Answers

Is 10% larger or smaller than 1/5? 10% means 10 out of 100, or 1 in every 10. 10% is smaller than 1/5, which is the same as 1 in every 5. Would you rather have 10% or 1/5 of £100? Write the missing percentage in each of the bar models:

The percentages should total 100.

Now write the numbers of children in each category.

Write 10% of each price, then work out 40% of each price.

£3.40 10% = £0.34 (or 34p), so 40% = £1.36 £5.10 10% = £0.51 (or 51p ), so 40% = £2.04 £12.00 10% = £1.20, so 40% = £4.80 £9.90 10% = £0.99 (or 99p) , so 40% = £3.96

24 children Crisps 75%

Fruit 25%

60 children

Walk 20%

Cycle 50% Drive 30%

24 children Crisps

18 Fruit

6

60 children

Walk 12

Cycle 30

Drive 18

£3.40 £12.00 £9.90 £5.10

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Week 8, Day 3 Use equivalent fractions to find percentages. · ã Hamilton Trust Explore more Hamilton Trust Learning Materials at Week 8, Day 3 Use equivalent fractions to find percentages